cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-10 of 11 results. Next

A209486 Number of 5-bead necklaces labeled with numbers -n..n allowing reversal, with sum zero and avoiding the patterns z z+1 z+2 and z z-1 z-2.

Original entry on oeis.org

4, 38, 140, 390, 866, 1702, 3014, 4984, 7774, 11620, 16716, 23352, 31768, 42302, 55232, 70950, 89774, 112150, 138434, 169120, 204610, 245452, 292080, 345096, 404980, 472382, 547820, 631998, 725474, 829006, 943190, 1068832, 1206574
Offset: 1

Views

Author

R. H. Hardin, Mar 09 2012

Keywords

Comments

Row 5 of A209485.

Examples

			Some solutions for n=10:
  -8  -5 -10  -6  -7  -6  -7  -8  -9  -7  -6 -10  -9  -8  -9  -6
  -7  -4   1  -2  -4   0  -5  -5   9  -2   0   1  -1   0   2  -5
   2   9   3   6  -5  -6   0   2  -7   6   4  -6   7   4  -7   1
   3  -5  -4  -3   6   4   2   3  -3   2   0   7   2  -2  10   2
  10   5  10   5  10   8  10   8  10   1   2   8   1   6   4   8

Links

Crossrefs

Cf. A209485.

Formula

Empirical: a(n) = 2*a(n-1) - a(n-3) - 2*a(n-5) + 2*a(n-6) + a(n-8) - 2*a(n-10) + a(n-11).
Empirical g.f.: 2*x*(2 + 15*x + 32*x^2 + 57*x^3 + 62*x^4 + 59*x^5 + 34*x^6 + 13*x^7 + 2*x^8) / ((1 - x)^5*(1 + x)^2*(1 + x^2)*(1 + x + x^2)). - Colin Barker, Jul 10 2018

A209487 Number of 6-bead necklaces labeled with numbers -n..n allowing reversal, with sum zero and avoiding the patterns z z+1 z+2 and z z-1 z-2.

Original entry on oeis.org

11, 136, 731, 2606, 7179, 16660, 34233, 64220, 112263, 185506, 292759, 444680, 653957, 935472, 1306483, 1786806, 2398979, 3168444, 4123729, 5296612, 6722303, 8439626, 10491183, 12923536, 15787389, 19137752, 23034123, 27540670, 32726395
Offset: 1

Views

Author

R. H. Hardin, Mar 09 2012

Keywords

Comments

Row 6 of A209485.

Examples

			Some solutions for n=8:
  -6  -8  -6  -7  -8  -7  -7  -8  -8  -4  -5  -6  -8  -8  -6  -8
  -1  -3  -6  -6  -2   0  -5   0  -4  -3   3  -2   1  -2  -3   3
   2  -1   0   6   6   6   2  -2  -5   6  -2   3  -4   7  -4  -4
  -2  -1  -3   2  -1  -7   5  -3   8  -3  -4   6  -3  -4   4   6
   6   6   7   4   6   6   6   5   8  -4   2  -3   8   4   1  -1
   1   7   8   1  -1   2  -1   8   1   8   6   2   6   3   8   4

Links

Formula

Empirical: a(n) = 5*a(n-1) - 10*a(n-2) + 11*a(n-3) - 10*a(n-4) + 11*a(n-5) - 10*a(n-6) + 5*a(n-7) - a(n-8) for n > 9.

A209488 Number of 7-bead necklaces labeled with numbers -n..n allowing reversal, with sum zero and avoiding the patterns z z+1 z+2 and z z-1 z-2.

Original entry on oeis.org

15, 458, 3740, 17771, 60778, 168453, 401634, 857433, 1679810, 3074315, 5321674, 8796771, 13984178, 21501971, 32119660, 46785813, 66648788, 93089119, 127741326, 172532039, 229703658, 301856427, 391974770, 503474661, 640230118, 806627193
Offset: 1

Views

Author

R. H. Hardin, Mar 09 2012

Keywords

Comments

Row 7 of A209485.

Examples

			Some solutions for n=5:
  -3  -4  -4  -4  -4  -4  -2  -5  -4  -4  -5  -4  -4  -5  -4  -5
  -1  -1  -4  -3   0  -3  -1  -4  -4  -2   5   2  -2  -4   1  -1
  -2   0   2   4  -1  -1  -2   5  -4   2  -4   3   0   5   1   3
   4  -2   2  -3   4  -1   0   3   2   1  -2  -3   1   0  -3  -5
  -3   3   3   4   0   4   3  -5   5  -3  -2  -1   4   1   1   4
   0   4  -3   1   1   5  -2   1   1   3   3  -1  -1  -1   1   5
   5   0   4   1   0   0   4   5   4   3   5   4   2   4   3  -1

Links

Formula

Empirical: a(n) = 2*a(n-1) - a(n-3) - a(n-5) + a(n-6) - 2*a(n-7) + 2*a(n-8) + a(n-9) - a(n-13) - 2*a(n-14) + 2*a(n-15) - a(n-16) + a(n-17) + a(n-19) - 2*a(n-21) + a(n-22) for n > 24.

A209477 Number of n-bead necklaces labeled with numbers -n..n allowing reversal, with sum zero and avoiding the patterns z z+1 z+2 and z z-1 z-2.

Original entry on oeis.org

1, 3, 7, 72, 866, 16660, 401634, 11891268, 413867410, 16583242015
Offset: 1

Views

Author

R. H. Hardin, Mar 09 2012

Keywords

Comments

Diagonal of A209485.

Examples

			Some solutions for n=6:
.-6...-3...-6...-6...-6...-6...-6...-4...-6...-6...-6...-6...-2...-6...-6...-5
..2...-2...-1....0....4....2...-4...-4....2....0...-4....0...-1...-4...-1...-3
..6....0...-2....0....0....2....5...-2...-2....1....1...-2....1....1....3....0
.-5....0....4...-2...-3....2....0....2....1....0....5...-2...-1....1....3....3
.-2....6....2....3...-1...-4....2....4....0....5....3....5....1....5...-2....6
..5...-1....3....5....6....4....3....4....5....0....1....5....2....3....3...-1

A209478 Number of n-bead necklaces labeled with numbers -1..1 allowing reversal, with sum zero and avoiding the patterns z z+1 z+2 and z z-1 z-2.

Original entry on oeis.org

1, 2, 1, 4, 4, 11, 15, 43, 77, 199, 423, 1080, 2514, 6355, 15529, 39429, 98875, 252551, 643133, 1653677, 4254070, 11005241, 28518931, 74179434, 193328017, 505236093, 1322919905, 3471492272, 9125743338
Offset: 1

Views

Author

R. H. Hardin, Mar 09 2012

Keywords

Comments

Column 1 of A209485.

Examples

			Some solutions for n=10:
.-1...-1...-1...-1...-1...-1...-1...-1...-1...-1...-1...-1...-1...-1...-1...-1
.-1....0...-1...-1...-1....0...-1...-1....0....0....0....0...-1...-1...-1...-1
..1....0....0....0....1....0....1....1...-1...-1...-1....0...-1....0....0....0
.-1...-1....0....0...-1...-1...-1...-1....1....1....1....1....1....0....0....0
..0....0....0....1....1....0....0....0...-1...-1....0...-1...-1....1....0....0
..0....0....0....1...-1....0....0....0....0....1....0....0....1....0....0....0
..0....0....0...-1....1....1...-1....0....0...-1...-1....0....1....0....1....1
..0....0....1...-1...-1....0....1....1....1....1....1....1....0...-1...-1....1
..1....1....0....1....1....0....1....0....0....0....0....0....0....1....1....0
..1....1....1....1....1....1....1....1....1....1....1....0....1....1....1....0

A209479 Number of n-bead necklaces labeled with numbers -2..2 allowing reversal, with sum zero and avoiding the patterns z z+1 z+2 and z z-1 z-2.

Original entry on oeis.org

1, 3, 4, 15, 38, 136, 458, 1781, 6912, 28141, 115761, 485607, 2056341, 8800541, 37945282, 164766522, 719617100, 3159529303, 13936202144
Offset: 1

Views

Author

R. H. Hardin, Mar 09 2012

Keywords

Comments

Column 2 of A209485.

Examples

			Some solutions for n=10:
.-2...-2...-2...-2...-2...-2...-2...-2...-2...-2...-2...-2...-2...-2...-2...-2
.-1....0...-2...-2....0...-1...-1...-2...-1...-2...-2...-2...-1....1....0....0
..1...-1....0....1....0...-1....1....0....2...-1....0...-1...-1...-1...-1....0
.-2...-1....0....2...-2....2...-2...-2....0....2....1....1...-1....0....2....2
.-1....0....2...-1....0....0....2....2...-1....1....1....2....2....0...-2...-1
..2...-1...-1...-2....2....0....2....1....1...-2....2....2....0....2....2....0
..0....2....2....1....1....1...-2...-1....1....0....2....2....2...-1....2...-1
..2....2...-2....2....2....1....0....0....1....2...-2...-1....2....0...-1...-1
..0....0....2...-1...-2....0....1....2...-2....2...-1...-1...-1...-1...-1....2
..1....1....1....2....1....0....1....2....1....0....1....0....0....2....1....1

A209480 Number of n-bead necklaces labeled with numbers -3..3 allowing reversal, with sum zero and avoiding the patterns z z+1 z+2 and z z-1 z-2.

Original entry on oeis.org

1, 4, 7, 35, 140, 731, 3740, 20888, 118137, 687981, 4059192, 24292229, 146840708, 895753665, 5505619880, 34065921090
Offset: 1

Views

Author

R. H. Hardin, Mar 09 2012

Keywords

Comments

Column 3 of A209485.

Examples

			Some solutions for n=8:
.-3...-2...-3...-3...-3...-3...-3...-3...-3...-2...-3...-3...-3...-3...-3...-3
.-2...-2...-1...-1....0...-3....1....0...-1...-1...-2....0...-1...-1...-2...-3
..0....0...-3....1...-1...-1...-1...-2....2...-2....0....3....2....0....1...-1
..3....3....1....1....3...-1...-2....2....3...-1....1...-2....0...-3...-1....3
..3...-2....2....1....2....3....1....3....1....3....3....2....2....2...-2....3
.-2....1....0....0....0....1....1....1....0....0....2....2....1...-1....3...-3
..1....0....2....0...-3....2....2...-2...-3....0...-3...-3...-2....3....3....1
..0....2....2....1....2....2....1....1....1....3....2....1....1....3....1....3

A209481 Number of n-bead necklaces labeled with numbers -4..4 allowing reversal, with sum zero and avoiding the patterns z z+1 z+2 and z z-1 z-2.

Original entry on oeis.org

1, 5, 12, 72, 390, 2606, 17771, 128598, 950292, 7180767, 55056590, 427567892, 3354737555, 26555548849
Offset: 1

Views

Author

R. H. Hardin, Mar 09 2012

Keywords

Comments

Column 4 of A209485.

Examples

			Some solutions for n=7:
.-3...-4...-3...-4...-3...-4...-4...-3...-2...-4...-4...-3...-2...-4...-3...-1
.-2...-2...-2...-3...-1...-1....1...-1...-2....2....2...-3...-2....2....2...-1
..4....3....4....0....0....4....1....4...-2...-4....1...-2....1....1...-2...-1
..0....1....2....4....3...-3...-1...-2....0....3...-2....0...-2...-3....2....0
.-1...-1...-2....2....2....1....1...-1....2...-4....2....3...-1...-2....0....0
..3...-1....0...-1...-2....2....1...-1....1....3...-2....2....2....3...-1...-1
.-1....4....1....2....1....1....1....4....3....4....3....3....4....3....2....4

A209482 Number of n-bead necklaces labeled with numbers -5..5 allowing reversal, with sum zero and avoiding the patterns z z+1 z+2 and z z-1 z-2.

Original entry on oeis.org

1, 6, 17, 128, 866, 7179, 60778, 541494, 4926728, 45758958, 431242307, 4115192739
Offset: 1

Views

Author

R. H. Hardin, Mar 09 2012

Keywords

Comments

Column 5 of A209485.

Examples

			Some solutions for n=7:
.-3...-4...-2...-5...-5...-4...-4...-5...-4...-4...-3...-4...-3...-5...-3...-4
.-3....0...-1...-2...-2....1....0...-1...-3...-3...-2...-2...-3...-5...-2...-2
..0....0....2....4....3....0....1...-3....1...-1....2...-1....4...-2...-2....5
..3....0....2....1....4....1...-2....3....4....4...-1....1...-1....2...-1....3
.-2...-1...-1....1...-4...-4....4....1....0....0....2....1....0....0....3...-4
..2....2...-2....0....2....1...-3....5....2....3...-3....4...-1....5....2....1
..3....3....2....1....2....5....4....0....0....1....5....1....4....5....3....1

Crossrefs

Cf. A209485.

A209483 Number of n-bead necklaces labeled with numbers -6..6 allowing reversal, with sum zero and avoiding the patterns z z+1 z+2 and z z-1 z-2.

Original entry on oeis.org

1, 7, 24, 205, 1702, 16660, 168453, 1778878, 19211780, 211576925, 2364602172, 26755001917
Offset: 1

Views

Author

R. H. Hardin, Mar 09 2012

Keywords

Comments

Column 6 of A209485.

Examples

			Some solutions for n=6:
.-6...-4...-4...-4...-4...-5...-3...-5...-5...-5...-5...-6...-2...-2...-2...-6
.-3...-1...-4...-1...-1....0...-2....1...-3...-4....0...-1...-1....0...-2...-4
.-3....3....0....5....1....3...-3...-2...-2....0...-1...-3....1....0....3....3
..1....2...-1...-3...-1...-4...-1...-1...-2....6....5....1....1...-1...-2...-4
..5...-4....6...-2....3....1....4....4....6....4...-1....3...-1...-1...-2....6
..6....4....3....5....2....5....5....3....6...-1....2....6....2....4....5....5
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